Question

Descompuneți în factori :
a) x la 4 + x la 3 +2x la 2 + x +1
b) 3x la 3 + 2x la 2 -3x -2

Answer 1

a)
x^4 + x^3 + x^2 + x^2 + x + 1 =
x^2(x^2 + x + 1) + (x^2 + x + 1)=
(x^2 + x + 1)(x^2 + 1)
b)
3x^3 + 2x^2 - 3x - 2 = 
3x^3 - 3x + 2x^2 - 2 = 
3x(x^2 - 1) + 2(x^2 - 1) =
(x^2 - 1)(3x + 2) = 
(x + 1)(x - 1)(3x + 2) 

Answer 2

x4+x3+2x2+x+1= x4+x3+x2+ x2+x+1= x2(x2+x+1) + (x2+x+1) = (x2+x+1)(x2+1)

3x3+2x2-3x-2 = x2(3x+2) –(3x+2) =(3x+2)(x2-1)= (3x+2)(x-1)(x+1)